Stochastic dynamic programming with factored representations

Markov decision processes (MDPs) have proven to be popular models for decision-theoretic planning, but standard dynamic programming algorithms for solving MDPs rely on explicit, state-based specifications and computations. To alleviate the combinatorial problems associated with such methods, we propose new representational and computational techniques for MDPs that exploit certain types of problem structure. We use dynamic Bayesian networks (with decision trees representing the local families of conditional probability distributions) to represent stochastic actions in an MDP, together with a decision-tree representation of rewards. Based on this representation, we develop versions of standard dynamic programming algorithms that directly manipulate decision-tree representations of policies and value functions. This generally obviates the need for state-by-state computation, aggregating states at the leaves of these trees and requiring computations only for each aggregate state. The key to these algorithms is a decision-theoretic generalization of classic regression analysis, in which we determine the features relevant to predicting expected value. We demonstrate the method empirically on several planning problems, Some parts of this report appeared in preliminary form in “Exploiting Structure in Policy Construction,” Proc. of Fourteenth International Joint Conf. on Artificial Intelligence (IJCAI-95), Montreal, pp.1550–1556(1995); and “Correlated Action Effects in DecisionTheoretic Regression,” Proc. of Thirteenth Conf. on Uncertainty in Artificial Intelligence (UAI-97), Providence, pp.30–37 (1997). yCommunicating author